Could humanity have entered the space age without relativity theory or quantum physics? (Other non-Newtonian physics would be allowed, it is actually the importance, or lack thereof, of relativity and quantum mechanics for space exploration which I want to highlight here)
With a "space age" I mean things like sending crewed Sputniks to LEO, landing men on the Moon, sending probes to outer planets, putting communication satellites in geostationary orbit, space telescopes in Lagrange points and such stuff which has been done today.
AFAIK a GPS system would have had some (manageble?) errors, and interplanetary trajectories would've been a bit off. But could such little mysteries not have been practically handled with some engineering rule of thumb adjustments as you go?
What would the greatest problems have been for a purely Newtonian space age humanity?